Finite Group Databasebeta

← Group #70616

Character table — Group #70616

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order12222222344446666666444488881212121224242424242424244444441212121212121212444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91-1111-1-1-111-1-1111-1-1-11-1ii−i−i11-1-11-1-111111-1-1-1-111-1-1i−iii−i−iii−i−i1-1ii−i−i11-1-1i−i
χ101-1111-1-1-111-1-1111-1-1-11-1ii−i−i11-1-11-1-111111-1-1-1-1-1-111i−iii−i−iii−i−i-11−i−iii-1-111−ii
χ111-1111-1-1-111-1-1111-1-1-11-1ii−i−i-1-1111-1-11-1-1-1-1111111-1-1−iiii−i−i−i−iii1-1ii−i−i-1-111−ii
χ121-1111-1-1-111-1-1111-1-1-11-1ii−i−i-1-1111-1-11-1-1-1-11111-1-111−iiii−i−i−i−iii-11−i−iii11-1-1i−i
χ131-1111-1-1-111-1-1111-1-1-11-1−i−iii11-1-11-1-111111-1-1-1-111-1-1−ii−i−iii−i−iii1-1−i−iii11-1-1−ii
χ141-1111-1-1-111-1-1111-1-1-11-1−i−iii11-1-11-1-111111-1-1-1-1-1-111−ii−i−iii−i−iii-11ii−i−i-1-111i−i
χ151-1111-1-1-111-1-1111-1-1-11-1−i−iii-1-1111-1-11-1-1-1-1111111-1-1i−i−i−iiiii−i−i1-1−i−iii-1-111i−i
χ161-1111-1-1-111-1-1111-1-1-11-1−i−iii-1-1111-1-11-1-1-1-11111-1-111i−i−i−iiiii−i−i-11ii−i−i11-1-1−ii
χ17222222222-2-2-2-2222222200000000-2-2-2-20000000022220000000000-2-20000000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-2-2-20000000000220000000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000221111-1-1-1-1000000000000
χ23222-2-2-22-2222-2-2-2-222-22-20000000022-2-20000000000000000000000002-22-2000000
χ24222-2-2-22-2222-2-2-2-222-22-20000000022-2-2000000000000000000000000-22-22000000
χ25222-2-2-22-22-2-222-2-222-22-22i−2i2i−2i0000-2-222000000000000002i−2i2i−2i0000000000000000
χ26222-2-2-22-22-2-222-2-222-22-2−2i2i−2i2i0000-2-22200000000000000−2i2i−2i2i0000000000000000
χ27222-2-2-22-2-1-2-22211-1-11-112i−2i2i−2i000011-1-1−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−3000000000000
χ28222-2-2-22-2-1-2-22211-1-11-112i−2i2i−2i000011-1-1i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−33000000000000
χ29222-2-2-22-2-1-2-22211-1-11-11−2i2i−2i2i000011-1-1−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−33000000000000
χ30222-2-2-22-2-1-2-22211-1-11-11−2i2i−2i2i000011-1-1i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−3000000000000
χ3122-22-22-2-2200002-22-2-2-2200002−22−200002−22−22−22−22i−2i2i−2i0000000000000000−i2i2−i2i200
χ3222-22-22-2-2200002-22-2-2-2200002−22−200002−22−22−22−2−2i2i−2i2i0000000000000000i2−i2i2−i200
χ3322-22-22-2-2200002-22-2-2-220000−22−220000−22−22−22−222i−2i2i−2i0000000000000000i2−i2i2−i200
χ3422-22-22-2-2200002-22-2-2-220000−22−220000−22−22−22−22−2i2i−2i2i0000000000000000−i2i2−i2i200
χ352-2222-2-2-22-222-222-2-2-22-200000000-222-20000000022-2-20000000000-220000000000
χ362-2222-2-2-22-222-222-2-2-22-200000000-222-200000000-2-22200000000002-20000000000
χ372-2222-2-2-2-12-2-22-1-1111-112i2i−2i−2i22-2-2-111-1-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ382-2222-2-2-2-12-2-22-1-1111-112i2i−2i−2i-2-222-111-11111-1-1-1-10000−2i2i−i−iiiii−i−i000000000000
χ392-2222-2-2-2-12-2-22-1-1111-11−2i−2i2i2i22-2-2-111-1-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ402-2222-2-2-2-12-2-22-1-1111-11−2i−2i2i2i-2-222-111-11111-1-1-1-100002i−2iii−i−i−i−iii000000000000
χ412-22-2-22-2222-22-2-2-2-2-2222000000002-22-20000000000000000000000002i−2i−2i2i000000
χ422-22-2-22-2222-22-2-2-2-2-2222000000002-22-2000000000000000000000000−2i2i2i−2i000000
χ432-22-2-22-222-22-22-2-2-2-22222-2-220000-22-22000000000000002-2-220000000000000000
χ442-22-2-22-222-22-22-2-2-2-2222-222-20000-22-2200000000000000-222-20000000000000000
χ452-22-2-22-22-1-22-221111-1-1-12-2-2200001-11-1−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i3000000000000
χ462-22-2-22-22-1-22-221111-1-1-12-2-2200001-11-1i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i3000000000000
χ472-22-2-22-22-1-22-221111-1-1-1-222-200001-11-1−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i3000000000000
χ482-22-2-22-22-1-22-221111-1-1-1-222-200001-11-1i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i3000000000000
χ492-2-22-2-222200002-2-222-2-200002−2−2200002−22−2−22−222i−2i−2i2i0000000000000000−i2i2i2−i200
χ502-2-22-2-222200002-2-222-2-200002−2−2200002−22−2−22−22−2i2i2i−2i0000000000000000i2−i2−i2i200
χ512-2-22-2-222200002-2-222-2-20000−222−20000−22−222−22−22i−2i−2i2i0000000000000000i2−i2−i2i200
χ522-2-22-2-222200002-2-222-2-20000−222−20000−22−222−22−2−2i2i2i−2i0000000000000000−i2i2i2−i200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ54444-4-4-44-4-244-4-422-2-22-2200000000-2-2220000000000000000000000000000000000
χ5544-44-44-4-4-20000-22-2222-2000022−2222−220000−22−22−22−2200000000000000000000000000
χ5644-44-44-4-4-20000-22-2222-20000−2222−222200002−22−22−22−200000000000000000000000000
χ5744-4-44-4-4440000-444-44-4-40000000000000000000000000000000000000000000000
χ5844-4-44-4-44-200002-2-22-222000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5944-4-44-4-44-200002-2-22-222000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ604-4444-4-4-4-2-444-4-2-2222-22000000002-2-220000000000000000000000000000000000
χ614-44-4-44-44-24-44-42222-2-2-200000000-22-220000000000000000000000000000000000
χ624-4-44-4-444-20000-222-2-222000022−22−22220000−22−222−22−200000000000000000000000000
χ634-4-44-4-444-20000-222-2-2220000−222222−2200002−22−2−22−2200000000000000000000000000
χ644-4-4-4444-440000-44-44-4-440000000000000000000000000000000000000000000000
χ654-4-4-4444-4-200002-22-222-2000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ664-4-4-4444-4-200002-22-222-2000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000

Here i is the imaginary unit (i² = −1).